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General projection systems and relaxed cocoercive nonlinear variational inequalities

Published online by Cambridge University Press:  17 February 2009

Ram U. Verma
Affiliation:
Department of Mathematics University of ToledoToledo Ohioverma99@msn.com.
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Abstract

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We explore the solvability of a general system of nonlinear relaxed cocoercive variational inequality (SNVI) problems based on a new projection system for the direct product of two nonempty closed and convex subsets of real Hilbert spaces.

Type
Articles
Copyright
Copyright © Australian Mathematical Society 2007

References

[1] Chang, S.S., Cho, Y.J. and Kim, J.K., “On the two-step projection methods and applications to variational inequalities”, Math. Inequal. Appl., accepted.Google Scholar
[2] Liu, L.S., “Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces”, J Math Anal Appl 194 (1995) 114127.CrossRefGoogle Scholar
[3] Liu, Z., Ume, J.S. and Kang, S.M., “Generalized nonlinear variational-like inequalities in reflexive Banach spaces”, J Optim Theory Appl 126 (2005) 157174.CrossRefGoogle Scholar
[4] Nie, H., Liu, Z., Kim, K.H. and Kang, S.M., “A system of nonlinear variational inequalities involving strongly monotone and pseudocontractive mappings”, Adv Nonlinear Var Inequal 6 (2003) 9199.Google Scholar
[5] Verma, R.U., “Nonlinear variational and constrained hemivariational inequalities”, ZAMM: Z Angew Math Mech 77 (1997) 387391.CrossRefGoogle Scholar
[6] Verma, R.U., “Projection methods, algorithms and a new system of nonlinear variational inequalities”, Comput Math Appl 41 (2001) 10251031.CrossRefGoogle Scholar
[7] Verma, R.U., “Generalized convergence analysis for two-step projection methods and applications to variational problems”, Appl Math Lett 18 (2005) 12861292.CrossRefGoogle Scholar
[8] Wittmann, R., “Approximation of fixed points of nonexpansive mappings”, Arch Math (Basel) 58 (1992)486491.CrossRefGoogle Scholar
[9] Zeidler, E., Nonlinear Functional Analysis and its Applications II/B(Springer-Verlag, New York, 1990).Google Scholar